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Over the last two decades the field of network science has been evolving fast. Many useful applications in a wide variety of disciplines have been found. The application of network science to the brain initiated the interdisciplinary field of complex brain networks. On a macroscopic level, brain regions are taken as nodes in a network. The analysis of pairwise connections between the brain regions as links has provided a new perspective on many problems. The application of network science to neuroscience data helped, for example, to identify the disruptions due to different neurological disorders when comparing healthy and abnormal brain networks. In this dissertation, we focus on the macroscopic level of brain regions and analyze their pairwise connections from a network science perspective. We address different general research questions from network science and exploit their application possibilities towards brain networks. Due to different measurement techniques, one can construct many different representations of brain networks. We thereby distinguish between the structural and functional brain network. Structural brain networks map the anatomical connections between the regions, which we could interpret as the ’streets’ of the brain. On top of these streets, we can measure the traffic with techniques like e.g. magnetoencephalography (MEG) or functional Magnetic Resonance Imaging (fMRI) resulting in so-called functional brain networks. However, the relation between the structural and the functional brain networks is still insufficiently understood. The first main research question of this dissertation focuses on the functional network layer and tries to identify the most important links and motifs of these networks. For this purpose, we propose the union of shortest path trees (USPT) as a new sampling method extracting all the shortest paths of a network (Chapter 2 and 3). After constructing the USPT, we compare the individual functional brain networks of multiple sclerosis patients and healthy controls (Chapter 2). Furthermore, we generalize this sampling method and present a new ranking of all the links based on the USPT (Chapter 3). Regarding the higher-order building blocks of the functional brain networks, we analyze the so-called information flow motifs based on MEG data from different frequency bands (Chapter 4). After researching the local properties of the functional brain networks, we analyze the influence of the underlying structural connections on the emerging information flow. Thus, the second main research question concerns the relationship between the functional and the underlying structural connectivity. Specifically, we analyze which topological properties of the structural networks drive the functional interactions. First, this question is approached in a mathematical and straightforward manner by assuming that an analytic function between the two networks exists (Chapter 5). We investigate this mapping function and its reverse by evaluating empirical individual and group-averaged multimodal data sets. A second approach towards the structure-function relationship employs a simple model of activity spread. The epidemic spreading model is applied on the human connectome to investigate the global patterns of directional information flow in brain networks (Chapter 6). The main focus here lies on the pairwise measure of transfer entropy to investigate the influence of one brain region on another. We present the results for the local and global outcomes of the dynamic spreading process aiming to identify the driving structural properties behind the observed global patterns.